Thread: Mathematical Induction Question

Hello, I have this problem that I can't figure out. I don't think I have too much issue with a simple version of maths induction but this particular question I can't seem to figure out.

The question is:

Use mathematical induction to prove that for every positive integer

n

1^

3 + 2^3 + 3^3 + . . . + n^3 = ((n (n + 1))/2)^2

I can only get to this stage:

((n(n + 1))/2)^2 + (n + 1)^3 = (((n + 1)((n + 1) + 1))/2)^2

I would greatly appreciate it if some wiz could help me out.

Thanks.

Originally Posted by madmunk

Hello, I have this problem that I can't figure out. I don't think I have too much issue with a simple version of maths induction but this particular question I can't seem to figure out.

The question is:

Use mathematical induction to prove that for every positive integer

n

1^

3 + 2^3 + 3^3 + . . . + n^3 = ((n (n + 1))/2)^2

I can only get to this stage:

((n(n + 1))/2)^2 + (n + 1)^3 = (((n + 1)((n + 1) + 1))/2)^2

I would greatly appreciate it if some wiz could help me out.

Thanks.

Expand the left hand side:




Now the right hand side:




-Dan

Thanks Dan, I understand now.